Topological edge states in graphene from proximity effect

Placing graphene on transition-metal dichalcogenides can increase its spin-orbit coupling by orders of magnitude and leads to the formation of edge states protected against time-reversal scattering in zigzag ribbons. We investigate an effective model for such systems in the presence of proximity-induced exchange splitting, which breaks time reversal symmetry and allows for quantum anomalous Hall states. We show the chiral edge states for zigzag and armchair ribbons and prove their topological character by computing the Chern number. From the bulk gap closing and Chern number for a wide parameter space of staggered intrinsic spin-orbit coupling and uniform exchange splitting (and vice versa) we identify distinct topological phases with Chern number $\pm$2 ($\pm$1). By adding proximity-induced s-wave superconductivity to the system we get particle-hole symmetric doubling of the number of edge states and topological superconducting phases with Chern number $\pm$4 ($\pm$2).